This inention relates to a digital filter, and more particularly a digital filter which performs mathematical operations by using a read only memory device and a random access memory device.
A digital filter functions to digitally operate a binary coded sample signal which is obtained by sampling and quantizing an analogue signal so as to impart a desired filter characteristic to the signal. Such digital filter is widely used in various signal processing apparatus including modulation/demodulation devices (MODEM). Generally, the digital filter is constituted by such digital elements that can be formed into an integrated circuit as a shift register, a multiplier and an adder, and has better frequency response characteristics than an analogue filter.
In addition, it has such advantages that it can be manufactured to have a small size and that it is economical. However, the digital filter must use many multipliers so that its price is higher than it otherwise might be.
For this reason, a digital filter has been proposed which uses a read only memory device (ROM) instead of multipliers. Such digital filter is disclosed, for example, in U.S. Pat. No. 3,777,130 by Cloisier et al on Dec. 4, 1973, especially in FIG. 2. When the digital filter disclosed in this patent is applied to an automatic equalizing circuit of MODEM, the size of the ROM for storing a partial product ##EQU6## of a filter coefficient .alpha.i and a signal subset Zi.sup.j obtained from an input sample increase which is not advantageous.